Summary: A brief review of these terms and their differences.
The terms Believer, Christian, Disciple, Apostle and even Saint are related, and often interchangeable, but they certainly are not always synonymous. Too often people suppose those titles have the exact same meanings. That is not accurate.
Believers. The first use of the word “believed” is found in Genesis chapter 15, verse 6“And he (Abram) believed in the Lord, and He accounted it to him for righteousness. The words believe or believed are found many times in the Old Testament but not the term “Believer” except as described in the NIV version of First Kings chapter 18, verse 3 “Obadiah was a devout believer in the Lord.” However, most other bible versions of this verse use terms like “Feared, revered, devout and true follower”.
Among the different versions of the bible, there is more unity that the New Testament term “believer” is first found Acts 16, verse 1 “...whose mother was a Jewess and a believer. In John chapter 4, verse 41 “And many more believed because of His own word.” However, Matthew 5, verse 13 was certainly speaking of believers when he wrote, “You are the salt of the earth; but if the salt loses its flavor, how shall it be seasoned? It is then good for nothing but to be thrown out and trampled underfoot by men.” The terms believer or believers are referred to several times in the New Testament book of Matthew, John, Acts, Corinthians, Timothy, and Peter.
Biblically speaking, believers, by the power of the Holy Spirit, instantly become Christians by placing their faith in the Lord Jesus Christ. Christians are born again by the power of the Holy Spirit and without that saving Grace would never see heaven. (John chapter 3, verse 3) All Christians “belong to Christ” and strive daily to reflect Christ's teaching and Commandments. True Christians, as opposed to those only Christian by their own definition, can also be called believers, followers, disciples, or saints. A true Christian in Christ and possesses new life through the indwelling of the Holy Spirit. Because he or she believes in Christ, a Christian will also be an obedient Disciple. Paul describes the reality of taking up one’s cross and following the Lord: “I have been crucified with Christ and I no longer live, but Christ lives in me. The life I live in the body, I live by faith in the Son of God, who loved me and gave himself for me” (Galatians chapter 2 verse 20).
Christians. Did you know Jesus was never recorded using the word “Christian”? The first instance of the word Christian is found in the book of Acts: “The Disciples were first called Christians in Antioch” (Acts chapter 11, verses 2 through 6). The majority of Biblical scholars agree believers did not call themselves “Christians.” Most likely that term was bestowed on them by non-believers, probably as an insulting term of distinctness. Believers adopted the name “Christians” for themselves because they were subject to suffering and abuse in the name of Yeshua, e.g., the most common name for Jesus the Christ. The idea that the term Christian was originally a pejorative finds some support in the first epistle of First Peter chapter 4, verse 16, “However, if you suffer as a Christian, do not be ashamed, but praise God that you bear that name.”
Of course, the term “Christian” is not found in the Old Testaments writings. Three principle references to Christians in the New Testament are:
Acts chapter 11, verse 26, “And when he had found him, he brought him to Antioch. So it was that for a whole year they assembled with the church and taught a great many people. And the Disciples were first called Christians in Antioch.”
Acts chapter 26, verse 28 “Then Agrippa said to Paul, “You almost persuade me to become a Christian.”
1st Peter chapter 4 verse 16 “Yet if anyone suffers as a Christian, let him not be ashamed, but let him glorify God in this matter.”
Similarly, Christian(s) behaviors, freedom, inspiration and descriptions of home life are expressed by:
Romans 12, verse 9 “[behaviors] Let love be without dissimulation. Abhor that which is evil; cleave to that which is good..”
Galatians chapter 5, verse 1 “[freedom] Christ has set us free to enjoy our freedom. So remain strong in the faith. Don’t let the chains of slavery hold you again.”
Colossians chapter 4, verse 2 “[inspirations] “Devote yourselves to prayer, being watchful and thankful.”
Colossians chapter 3, verse 18-25 “[home life] “Wives, submit yourselves to your husbands, as is fitting in the Lord. Husbands, love your wives and do not be harsh with them. Children, obey your parents in everything, for this pleases the Lord. Fathers, do not embitter your children, or they will become discouraged.”
Both, Believers and Christians know Jesus the Christ is our personal Savior and follow the biblical teachings that there is only one God in all existence, God is manifested as a triune God, God the Father, Jesus the Son, and the Holy Spirit. We know salvation is by grace alone through faith, Jesus died on the cross, and Jesus rose from the dead in His glorified, physical, body. Any theological statements contradicting any of these teachings is not Christian. Therefore, all non-believers represent the Anti-Christ. There is no neutral ground. In First John chapter 4, verses 1 through 3, my interpretation is, John is saying all who do not confess Jesus are the spirit of the antichrist, "Beloved, do not believe every spirit, but test the spirits, whether they are of God; because many false prophets have gone out into the world. 2 By this you know the Spirit of God: Every spirit that confesses that Jesus Christ has come in the flesh is of God, 3 and every spirit that does not confess that Jesus Christ has come in the flesh is not of God. And this is the spirit of the Antichrist, which you have heard was coming, and is now already in the world."